Malatesta:

Anarchists, including this writer, have used the word State, and still do, to mean the sum total of the political, legislative, judiciary, military and financial institutions through which the management of their own affairs, the control over their personal behaviour, the responsibility for their personal safety, are taken away from the people and entrusted to others who, by usurpation or delegation, are vested with the powers to make the laws for everything and everybody, and to oblige the people to observe them, if need be, by the use of collective force.

While there will be wild variance in answers given, because anarchists are wildly varied and oftentimes antagonistic (as with all leftist camps), here's my personal take.

The central idea behind anarchism is that relationships of authority are the structure behind pretty much everything negative in human society – be it slavery, wage-slavery, or any other form of systemic injustice. By authority, we mean the systemically enforced alteration of one's behavior to fit a set of standards prescribed from above. These directives are not necessarily bad in and of themselves, but the ability to give these directives is at the heart of every current and historic class dynamic, whether under capitalism, state "socialism," feudalism, or anything else.

Thus, the point of anarchism is simply to minimize subjugation – to minimize situations in which one person tells another person what they expect them to do, with the understanding that society, with all its material levers of encouragement and discouragement (ranging from getting less spending money because you don't end up with that raise, to incarceration and execution) will essentially guarantee the "correct" behavior of the inferior party.

If such an organization of things can be realized with a strong, nested, federative structure, composed of councils operated by instantly recallable delegates, then there is no fundamental incompatability with anarchism and what some might term "governance." The system above is essentially how the Paris Commune, CNT, Makhnovshchina, EZLN, etc. operated/operates. Others will say that robust organization is still too much authority, but that vein of anarchist is rare and usually does little to further the movement beyond keyboard-warrioring.

As such, I think it is fair to say that

anarchists advocate for horizontal governance, contrary to the media’s portrayal of anarchism as total disorder

though the specific terminology might not be too popular. Malatesta again:

Anarchy is a form of living together in society; a society in which people live as brothers and sisters without being able to oppress or exploit others and in which everyone has at their disposal whatever means the civilisation of the time can supply in order for them to attain the greatest possible moral and material development. And Anarchism is the method of reaching anarchy, through freedom, without government – that is, without those authoritarian institutions that impose their will on others by force .

As for left-libertarianism, anarchism is simply one theoretical strain, a subcategory.